Neft Teacher · Learn It

Unit 8 · Standard 6.AT.8

Write and Solve Equations Using Addition or Subtraction

Lesson 8-2 · Learn It — how the math works

Why we're learning this

Detective Chen found a coded message: 'The suspect's locker number plus 23 equals 58.' She needs to figure out the locker number to crack the case. The equation is n + 23 = 58. What is n?

✱ Math Workbench

Learn It

How do I solve an addition or subtraction equation?

To solve means to find the value that makes the equation true. I use the inverse operation (the opposite) to get the variable alone, and I do the same thing to both sides.

Picture itSee what the math looks like before you read about it

The top row shows two baseballs and a bat with a total of 50. The bottom row shows one baseball and a bat with a total of 45. Compare the two rows.
Where you see this in real lifeThe top row shows two baseballs and a bat with a total of 50. The bottom row shows one baseball and a bat with a total of 45. Compare the two rows.

Watch me solve itI do — read one step at a time

The problem looks like this
A bar model: a bar for 58 split into an unknown part labelled n and a known part of 23. total = 58 n = ? 23 The unknown part and 23 together make 58.
  1. Solve n + 23 = 58. The 23 is added to n.n + 23 = 58
  2. The inverse of adding 23 is subtracting 23.
  3. I subtract 23 from both sides: n + 23 − 23 = 58 − 23.n + 23
  4. That leaves n = 35. Check: 35 + 23 = 58. True!35 + 23 = 58

Watch out — mistakes students make here

  • Subtract 2.8 from 9.1 — that's not the result.
  • Recheck your subtraction: 9.1 − 2.8 in the tenths place.
  • The discount was not added back fully. Set up d − 15 = 38, then add 15 to both sides and combine carefully.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Solve x − 4 = 9. Is x being added or subtracted?
  2. It is subtracted, so the inverse is adding 4 to both sides.
  3. x = 9 + 4 = 13. Check together: 13 − 4 = 9. True?x = 9 + 4 = 13

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Use the scale to solve n + 19 = 46 — a new , not the n + 23 = 58 we just watched.
  • Then solve the practice and check each answer.

Solve: A shirt costs $d. After a $15 discount, it costs $38. What is d?

My answer

Stuck? Open one hint at a time.

Hint 1

The $15 discount was taken OFF the original price d, and $38 is what's left after the discount.

Hint 2

Write the story first: d − 15 = 38. Then undo the subtraction — the original price should be MORE than $38, not less.

Hint 3

Add the $15 discount back onto the $38 sale price: d = 38 + 15. Which choice matches that total?

Check my answer
✅ Answer: $53
d − 15 = 38 → d = 38 + 15 = 53.

Turn & TalkSay it out loud with a partner

Detective Chen's clue is n + 23 = 58, where n is a locker number. Why can't she just 'know' n by looking, and what could she do to both sides to find it?

Try starting with:

  • The variable n is added to ___, so to find n I can ___.La variable n está sumada a ___, así que para hallar n puedo ___.
  • I would use ___ to undo the ___.Usaría ___ para deshacer la ___.
Use these wordsequationinverse operationisolatesolution